Of course there is no force to digitize maps! Your drawings look good in my opinion (but to clear that, I draw with Photoshop, so of course I am not the expert to handdrawings) as they are.

Although as a Photoshop and QGIS user I see some advantages in using software:
- mistakes could be easily "erased"
- effects (especially colors, papertype and the like) could be done afterwards and tried in many different ways without destroying your map
- management of maps (especially a whole mapset of one world) is easier

But that just might be a feeling of someone, who wholehearted works digital. However, if you want to try some software, I recommend to have a look into the tutorials section, where many great tutorials for different software (e.g. gimp and photoshop) are stored. They gave me a lot of help starting my own mapping and improving skills.